VARIATIONAL-PRINCIPLES DEVELOPED FOR AND APPLIED TO POROUS-ELASTIC SOLIDS

A dual variational principle is formulated for a general porous-elasti c material in Laplace transform space. The material may be anisotropic and spatially inhomogeneous. As an application of the theory, we cons ider two problems of a crack in an infinite strip of inhomogeneous roc k. In the first we bound the Stress Intensity Factor in both the trans form and real time domains. For the second, we place bounds on a funct ion of the poroelastic Stress Intensity Factor and pore pressure gradi ent coefficient, in transform space. The bounds are compared with an e ffective medium solution in both cases. We discuss the significance of the method with regard to bounding effective properties in non-static problems. We obtain, in implicit form, bounds on effective permeabili ty for a rigid porous solid in transform space. These suggest the effe ctive property is history dependent. Asymptotic methods are used to ob tain large and small time results.